Noun
hom-set (plural hom-sets)
(category theory) The set or collection of all morphisms from A to B for some given ordered pair (A, B) of objects from some given category.
Additivity If C and D are preadditive categories and F : C ← D is an additive functor with a right adjoint G : C → D, then G is also an additive functor and the hom-set bijections : are, in fact, isomorphisms of abelian groups. Source: Internet
A similar argument allows one to construct a hom-set adjunction from the terminal morphisms to a left adjoint functor. Source: Internet
Here composition of morphisms is just ring multiplication and the unique hom-set is the underlying abelian group. Source: Internet
In category theory Every poset (and every preorder ) may be considered as a category in which every hom-set has at most one element. Source: Internet
One can verify directly that this correspondence is a natural transformation, which means it is a hom-set adjunction for the pair (F,G). Source: Internet
In other words, each hom-set Hom(A,B) in C has the structure of an R -module, and composition of morphisms is R -bilinear. Source: Internet